Nearest just interval: Difference between revisions

Revision as of 20:46, 8 November 2010

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This revision was by author genewardsmith and made on 2010-11-08 20:46:24 UTC.

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An interval given by its logarithmic size measure (like [[cent]]s or amount of edo-atoms) has an infinite list of //nearest just intervals//

==Examples==
The 600-cent interval (6 steps of [[12edo]], "Tritone") approximates following ratios:
|| **freq. ratio** || **log([[Tenney Height]])** || **size** in cents || **"error"** in cents ||
|| ... || ... || ... || ... ||
||= 3 / 2 ||= 2.585 ||= 701.96 ||= 101.96 ||
||= 7 / 5 ||= 5.129 ||= 582.51 ||= 17.49 ||
||= 17 / 12 ||= 7.672 ||= 603.00 ||= 3.000 ||
|| ... || ... || ... || ... ||

The 300-cent interval (3 steps of [[12edo]], "minor third") approximates following ratios:
|| **freq. ratio** || **log([[Tenney Height]])** || **size** in cents || **"error"** in cents ||
|| ... || ... || ... || ... ||
||= 6 / 5 ||= 4.907 ||= 315.64 ||= 15.64 ||
||= 19 / 16 ||= 8.248 ||= 297.51 ||= 2.49 ||
||= 25 / 21 ||= 9.036 ||= 301.84 ||= 1.84 ||
|| ... || ... || ... || ... ||

Original HTML content:

<html><head><title>Nearest just interval</title></head><body>An interval given by its logarithmic size measure (like <a class="wiki_link" href="/cent">cent</a>s or amount of edo-atoms) has an infinite list of <em>nearest just intervals</em><br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Examples"></a><!-- ws:end:WikiTextHeadingRule:0 -->Examples</h2>
The 600-cent interval (6 steps of <a class="wiki_link" href="/12edo">12edo</a>, &quot;Tritone&quot;) approximates following ratios:<br />


<table class="wiki_table">
    <tr>
        <td><strong>freq. ratio</strong><br />
</td>
        <td><strong>log(<a class="wiki_link" href="/Tenney%20Height">Tenney Height</a>)</strong><br />
</td>
        <td><strong>size</strong> in cents<br />
</td>
        <td><strong>&quot;error&quot;</strong> in cents<br />
</td>
    </tr>
    <tr>
        <td>...<br />
</td>
        <td>...<br />
</td>
        <td>...<br />
</td>
        <td>...<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">3 / 2<br />
</td>
        <td style="text-align: center;">2.585<br />
</td>
        <td style="text-align: center;">701.96<br />
</td>
        <td style="text-align: center;">101.96<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">7 / 5<br />
</td>
        <td style="text-align: center;">5.129<br />
</td>
        <td style="text-align: center;">582.51<br />
</td>
        <td style="text-align: center;">17.49<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">17 / 12<br />
</td>
        <td style="text-align: center;">7.672<br />
</td>
        <td style="text-align: center;">603.00<br />
</td>
        <td style="text-align: center;">3.000<br />
</td>
    </tr>
    <tr>
        <td>...<br />
</td>
        <td>...<br />
</td>
        <td>...<br />
</td>
        <td>...<br />
</td>
    </tr>
</table>

<br />
The 300-cent interval (3 steps of <a class="wiki_link" href="/12edo">12edo</a>, &quot;minor third&quot;) approximates following ratios:<br />


<table class="wiki_table">
    <tr>
        <td><strong>freq. ratio</strong><br />
</td>
        <td><strong>log(<a class="wiki_link" href="/Tenney%20Height">Tenney Height</a>)</strong><br />
</td>
        <td><strong>size</strong> in cents<br />
</td>
        <td><strong>&quot;error&quot;</strong> in cents<br />
</td>
    </tr>
    <tr>
        <td>...<br />
</td>
        <td>...<br />
</td>
        <td>...<br />
</td>
        <td>...<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">6 / 5<br />
</td>
        <td style="text-align: center;">4.907<br />
</td>
        <td style="text-align: center;">315.64<br />
</td>
        <td style="text-align: center;">15.64<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">19 / 16<br />
</td>
        <td style="text-align: center;">8.248<br />
</td>
        <td style="text-align: center;">297.51<br />
</td>
        <td style="text-align: center;">2.49<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">25 / 21<br />
</td>
        <td style="text-align: center;">9.036<br />
</td>
        <td style="text-align: center;">301.84<br />
</td>
        <td style="text-align: center;">1.84<br />
</td>
    </tr>
    <tr>
        <td>...<br />
</td>
        <td>...<br />
</td>
        <td>...<br />
</td>
        <td>...<br />
</td>
    </tr>
</table>

</body></html>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2010-06-06 17:30:51 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-11-08 20:46:24 UTC</tt>.<br>
-: The original revision id was <tt>147268909</tt>.<br>
+: The original revision id was <tt>177695703</tt>.<br>
 : The revision comment was: <tt></tt><br>
 The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
 <h4>Original Wikitext content:</h4>
-<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">An interval given by its logarhithmic size measure (like [[cent]]s or amount of edo-atoms) has an infinite list of //nearest just intervals//
+<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">An interval given by its logarithmic size measure (like [[cent]]s or amount of edo-atoms) has an infinite list of //nearest just intervals//
 ==Examples==
@@ Line 26: / Line 26: @@
 </pre></div>
 <h4>Original HTML content:</h4>
-<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Nearest just interval&lt;/title&gt;&lt;/head&gt;&lt;body&gt;An interval given by its logarhithmic size measure (like &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s or amount of edo-atoms) has an infinite list of &lt;em&gt;nearest just intervals&lt;/em&gt;&lt;br /&gt;
+<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Nearest just interval&lt;/title&gt;&lt;/head&gt;&lt;body&gt;An interval given by its logarithmic size measure (like &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s or amount of edo-atoms) has an infinite list of &lt;em&gt;nearest just intervals&lt;/em&gt;&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Examples"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Examples&lt;/h2&gt;

Nearest just interval: Difference between revisions

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